I think I see your disconnect. You file a credit form when you have a tax liability for another state, not for withholdings.
When you enter the W2 into the program, the federal information should match, the state information is where you explain what really happened.
Part year for PA should have your dates of residency and the income earned while living in PA. You can look at paystubs or the W2 may have the correct information. Enter the correct PA information for wages and tax withheld.
The CT/NY issue is bothering you. There are two ways this can go.
1. You file CT and say none of the wages were taxable and get back the full amount. There is no NY credit since there is no CT tax liability.
2. You file CT and have an actual tax liability then you would file a credit on your NY return for the taxes paid to CT.
Unless you are part owner of the business, you would not have CT source income and would have no CT income tax liability unless you have other income from CT, like a pension distribution, Powerball, etc. See CT source income for nonresidents
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